Answer: 4 grocery stores

We are given that the bins start at 0.8 and have a width of 0.1, which means one of the bins has endpoints 1.3 and 1.4. This bin (the tallest bar) includes all grocery stores that sold broccoli for a price greater than or equal to $1.30 per pound, but less than $1.40 per pound.

This bar has a width of 0.1 and we’d estimate the height to be around 2.2, though we can’t say exactly. Multiplying these values, the area of the bar is about 0.22, which means about 22 percent of the grocery stores fall into this bin. There are 18 grocery stores in total, as we are told in the introduction to this question. We can compute using a calculator that 22 percent of 18 is 3.96. Since the actual number of grocery stores this represents must be a whole number, this bin must represent 4 grocery stores.

The reason for the slight discrepancy between 3.96 and 4 is that we used 2.2 for the height of the bar, a number that we determined by eye. We don’t know the exact height of the bar. It is reassuring to do the calculation and get a value that’s very close to an integer, since we know the final answer must be an integer.

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Difficulty: ⭐️⭐️⭐️

The average score on this problem was 71%.

Answer: 1.25

First, we need to figure out how many grocery stores the bin [\$1.10, \$1.50) contains. We already know from the previous subpart that there are four grocery stores in the bin [\$1.30, \$1.40). We could do similar calculations to find the number of grocery stores in each of these bins:

• [\$1.10, \$1.20)
• [\$1.20, \$1.30)
• [\$1.40, \$1.50)

However, it’s much simpler and faster to use the fact that when the bins are all equally wide, the height of a bar is proportional to the number of data values it contains. So looking at the histogram in the previous subpart, since we know the [\$1.30, \$1.40) bin contains 4 grocery stores, then the [\$1.10, \$1.20) bin must contain 1 grocery store, since it’s only a quarter as tall. Again, we’re taking advantage of the fact that there must be an integer number of grocery stores in each bin when we say it’s 1/4 as tall. Our only options are 1/4, 1/2, or 3/4 as tall, and among those choices, it’s clear.

Therefore, by looking at the relative heights of the bars, we can quickly determine the number of grocery stores in each bin:

• [\$1.10, \$1.20): 1 grocery store
• [\$1.20, \$1.30): 3 grocery stores
• [\$1.30, \$1.40): 4 grocery stores
• [\$1.40, \$1.50): 1 grocery store

Adding these numbers together, this means there are 9 grocery stores whose broccoli prices fall in the interval [\$1.10, \$1.50). In the new histogram, these 9 grocery stores will be represented by a bar of width 1.50-1.10 = 0.4. The area of the bar should be \frac{9}{18} = 0.5. Therefore the height must be \frac{0.5}{0.4} = 1.25.

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Difficulty: ⭐️⭐️⭐️⭐️

The average score on this problem was 33%.

Answer: Yes

When we use .plot without specifying a y column, it uses every column in the DataFrame as a y column and creates an overlaid plot. Since we first use get with the list ['broccoli', 'ice_cream'], this keeps the 'broccoli' and 'ice_cream' columns from prices, so our bar chart will overlay broccoli prices with ice cream prices. Notice that this get is unnecessary because prices only has these two columns, so it would have been the same to just use prices directly. The resulting bar chart will look something like this:

Each grocery store has its broccoli price represented by the length of the blue bar and its ice cream price represented by the length of the red bar. We can therefore answer the question by simply counting the number of red bars that are shorter than their corresponding blue bars.

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Difficulty: ⭐️⭐️

The average score on this problem was 78%.

Answer: No

This will create an overlaid histogram of broccoli prices and ice cream prices. So we will be able to see the distribution of broccoli prices together with the distribution of ice cream prices, but we won’t be able to pair up particular broccoli prices with ice cream prices at the same store. This means we won’t be able to answer the question. The overlaid histogram would look something like this:

This tells us that broadly, ice cream tends to be more expensive than broccoli, but we can’t say anything about the number of stores where ice cream is cheaper than broccoli.

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Difficulty: ⭐️⭐️

The average score on this problem was 81%.

Answer: Yes, and there are 2 such stores.

In this scatterplot, each grocery store is represented as one dot. The x-coordinate of that dot tells the price of broccoli at that store, and the y-coordinate tells the price of ice cream. If a grocery store’s ice cream price is cheaper than its broccoli price, the dot in the scatterplot will have y<x. To identify such dots in the scatterplot, imagine drawing the line y=x. Any dot below this line corresponds to a point with y<x, which is a grocery store where ice cream is cheaper than broccoli. As we can see, there are two such stores.

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Difficulty: ⭐️⭐️

The average score on this problem was 78%.

Answer:

To draw the histogram, we first need to bin the data and figure out how many data values fall into each bin. The code includes bins=np.arange(0, 7, 2) which means the bin endpoints are 0, 2, 4, 6. This gives us three bins: [0, 2), [2, 4), and [4, 6]. Remember that all bins, except for the last one, include the left endpoint but not the right. The last bin includes both endpoints.

Now that we know what the bins are, we can count up the number of values in each bin. We need to look at the 'Appearance_Order' column of sungod.take(np.arange(5)), or the first five rows of sungod. The values there are 1, 4, 3, 1, 3. The two 1s fall into the first bin [0, 2). The two 3s fall into the second bin [2, 4), and the one 4 falls into the last bin [4, 6]. This means the proportion of values in each bin are \frac{2}{5}, \frac{2}{5}, \frac{1}{5} from left to right.

To figure out the height of each bar in the histogram, we use the fact that the area of a bar in a density histogram should equal the proportion of values in that bin. The area of a rectangle is height times width, so height is area divided by width.

For the bin [0, 2), the area is \frac{2}{5} = 0.4 and the width is 2, so the height is \frac{0.4}{2} = 0.2.

For the bin [2, 4), the area is \frac{2}{5} = 0.4 and the width is 2, so the height is \frac{0.4}{2} = 0.2.

For the bin [4, 6], the area is \frac{1}{5} = 0.2 and the width is 2, so the height is \frac{0.2}{2} = 0.1.

Since the bins are all the same width, the fact that there an equal number of values in the first two bins and half as many in the third bin means the first two bars should be equally tall and the third should be half as tall. We can use this to draw the rest of the histogram quickly once we’ve drawn the first bar.

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Difficulty: ⭐️⭐️⭐️⭐️

The average score on this problem was 45%.

Answer: 80%

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Difficulty: ⭐️⭐️⭐️

The average score on this problem was 73%.

Answer: 90

Remember, the key property of histograms is that the proportion of values in a bin is equal to the area of the corresponding bar. To find the number of values in the range 2-8 (the x-axis is measured in hundreds), we’ll need to find the proportion of values in the range 2-8 and multiply that by 200, which is the total number of students in DSC 10. To find the proportion of values in the range 2-8, we’ll need to find the areas of the 2-4, 4-6, and 6-8 bars.

Area of the 2-4 bar: \text{width} \cdot \text{height} = 2 \cdot 0.1 = 0.2

Area of the 4-6 bar: \text{width} \cdot \text{height} = 2 \cdot 0.0625 = 0.125.

Area of the 6-8 bar: \text{width} \cdot \text{height} = 2 \cdot 0.0625 = 0.125.

Then, the total proportion of values in the range 2-8 is 0.2 + 0.125 + 0.125 = 0.45, so the total number of students with between 200 and 800 Instagram followers is 0.45 \cdot 200 = 90.

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Difficulty: ⭐️⭐️⭐️⭐️

The average score on this problem was 49%.

Answer: 400 \cdot h

As we said at the start of the last solution, the key property of histograms is that the proportion of values in a bin is equal to the area of the corresponding bar. Then, the number of students represented bar a bar is the total number of students in DSC 10 (200) multiplied by the area of the bar.

Since all bars in this histogram have a width of 2, the area of a bar in this histogram is \text{width} \cdot \text{height} = 2 \cdot h. If there are 200 students in total, then the number of students represented in a bar with height h is 200 \cdot 2 \cdot h = 400 \cdot h.

To verify our answer, we can check to see if it makes sense in the context of the previous subpart. The 2-4 bin has a height of 0.1, and 400 \cdot 0.1 = 40. The total number of students in the range 2-8 was 90, so it makes sense that 40 of them came from the 2-4 bar, since the 2-4 bar takes up about half of the area of the 2-8 range.

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Difficulty: ⭐️⭐️⭐️⭐️

The average score on this problem was 36%.

Answer: int(academic_year.split("-")[1])

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Difficulty: ⭐️⭐️⭐️

The average score on this problem was 70%.

Answer: 2019

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Difficulty: ⭐️⭐️

The average score on this problem was 87%.

Answer: takes a string as input, returns a string

To use the Series method .apply, we first need a Series, containing values of any type. We pass in the name of a function to .apply and essentially, .apply calls the given function on each value of the Series, producing a Series with the resulting outputs of those function calls. In this case, .apply(extract_product_line) is called on the Series ikea.get('product'), which contains string values. This means the function extract_product_line must take strings as inputs. We’re told that the code assigns a new column to the ikea DataFrame containing the product line associated with each product, and we know that the product line is a string, as it’s the first word of the product name. This means the function extract_product_line must output a string.

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Difficulty: ⭐️⭐️⭐️

The average score on this problem was 72%.

Answer: x.split(' ')[0]

This function should take as input a string x, representing a product name, and return the first word of that string, representing the product line. Since words are separated by spaces, we want to split the string on the space character ' '.

It’s also correct to answer x.split()[0] without specifying to split on spaces, because the default behavior of the string .split method is to split on any whitespace, which includes any number of spaces, tabs, newlines, etc. Since we’re only extracting the first word, which will be separated from the rest of the product name by a single space, it’s equivalent to split using single spaces and using the default of any whitespace.

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Difficulty: ⭐️⭐️

The average score on this problem was 84%.

Answer: int(first_split[0])*60+int(second_split[0])

As the last subpart demonstrated, if we want to compare times, it doesn’t make sense to do so when times are represented as strings. In the to_minutes function, we convert a time string into an integer number of minutes.

The first step is to understand the logic. Every hour contains 60 minutes, so for a time string formatted like x hr, y min' the total number of minutes comes from multiplying the value of x by 60 and adding y.

The second step is to understand how to extract the x and y values from the time string using the string methods .split. The string method .split takes as input some separator string and breaks the string into pieces at each instance of the separator string. It then returns a list of all those pieces. The first line of code, therefore, creates a list called first_split containing two elements. The first element, accessed by first_split[0] contains the part of the time string that comes before ' hr, '. That is, first_split[0] evaluates to the string x.

Similarly, first_split[1] contains the part of the time string that comes after ' hr, '. So it is formatted like 'y min'. If we split this string again using the separator of ' min', the result will be a list whose first element is the string 'y'. This list is saved as second_split so second_split[0] evaluates to the string y.

Now we have the pieces we need to compute the number of minutes, using the idea of multiplying the value of x by 60 and adding y. We have to be careful with data types here, as the bolded instructions warn us that the function must return an integer. Right now, first_split[0] evaluates to the string x and second_split[0] evaluates to the string y. We need to convert these strings to integers before we can multiply and add. Once we convert using the int function, then we can multiply the number of hours by 60 and add the number of minutes. Therefore, the solution is int(first_split[0])*60+int(second_split[0]).

Note that failure to convert strings to integers using the int function would lead to very different behavior. Let’s take the example time string of '3 hr, 5 min' as input to our function. With the return statement as int(first_split[0])*60+int(second_split[0]), the function would return 185 on this input, as desired. With the return statement as first_split[0]*60+second_split[0], the function would return a string of length 61, looking something like this '3333...33335'. That’s because the * and + symbols do have meaning for strings, they’re just different meanings than when used with integers.

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Difficulty: ⭐️⭐️⭐️

The average score on this problem was 71%.

Answer: Options 1 and 5

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Difficulty: ⭐️⭐️

The average score on this problem was 83%.

Answer: 30

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Difficulty: ⭐️⭐️⭐️

The average score on this problem was 55%.

Answer 35%

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Difficulty: ⭐️⭐️⭐️

The average score on this problem was 72%.