SAT One-Variable Data Question 50 | Free SAT Prep | Aniko

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Question 50·Medium·One-Variable Data Distributions; Measures of Center and Spread

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The numbers below show the daily customer counts for four different food trucks over a 7-day period.

Food Truck A: 5, 5, 6, 7, 8, 9, 50
Food Truck B: 1, 20, 21, 22, 23, 24, 25
Food Truck C: 10, 12, 14, 16, 18, 20, 22
Food Truck D: 15, 15, 16, 17, 18, 19, 20

For which food truck is the median number of customers greater than the mean?

When comparing median and mean on the SAT, first check if the data are already sorted; if so, grab the median quickly as the middle value (for 7 numbers, the 4th). Then compute the mean by summing and dividing, but keep an eye out for outliers: a very large value pushes the mean above the median, while a very small value pulls the mean below the median. Use that idea to predict which way the mean should move, and then confirm with quick calculations to save time and avoid errors.

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Start with medians

Each truck has 7 days of data already in increasing order. For 7 values, what position is the median in, and what is that number for each truck?

Then compute means

For each truck, add the 7 daily customer counts and divide by 7. Write down the approximate mean for each list.

Compare center measures

For each truck, compare its median to its mean: is the median less than, equal to, or greater than the mean?

Look for the effect of an outlier

Notice which lists have a very small or very large value compared with the rest. Think about how that extreme value affects the mean versus the median.

Desmos Guide

Compute the means in Desmos

For each truck, type the average as a single expression, for example for Food Truck A: (5+5+6+7+8+9+50)/7, for B: (1+20+21+22+23+24+25)/7, and similarly for C and D. Note the decimal output Desmos gives for each mean.

Compare Desmos means to the medians you found

Using the medians you read directly from the ordered lists (the 4th value in each), compare each median to the corresponding mean value shown in Desmos and identify which truck has its median larger than its displayed mean.

Step-by-step Explanation

Recall what median and mean are

For each list of 7 numbers:

The median is the 4th number when the data are in order (because 7 values have the middle at position $(7+1)/2=4$ ).
The mean is the sum of the 7 numbers divided by 7.

All four food trucks already have their data listed in increasing order, so the median is just the 4th value in each list.

Find the medians for each food truck

Identify the 4th value in each ordered list:

Food Truck A: $5, 5, 6, \mathbf{7}, 8, 9, 50$ → median $=7$
Food Truck B: $1, 20, 21, \mathbf{22}, 23, 24, 25$ → median $=22$
Food Truck C: $10, 12, 14, \mathbf{16}, 18, 20, 22$ → median $=16$
Food Truck D: $15, 15, 16, \mathbf{17}, 18, 19, 20$ → median $=17$

Keep these medians in mind for comparison after you find each mean.

Compute the mean customers for each truck

Now find the mean for each by adding the 7 numbers and dividing by 7.

Food Truck A: sum $=5+5+6+7+8+9+50=90$
- Mean $=90/7\approx12.86$
Food Truck B: sum $=1+20+21+22+23+24+25=136$
- Mean $=136/7\approx19.43$
Food Truck C: sum $=10+12+14+16+18+20+22=112$
- Mean $=112/7=16$
Food Truck D: sum $=15+15+16+17+18+19+20=120$
- Mean $=120/7\approx17.14$

Compare mean and median for each truck and choose the correct one

Compare the median and mean for each truck:

A: median $7$ , mean $\approx12.86$ → mean $>$ median
B: median $22$ , mean $\approx19.43$ → median $>$ mean
C: median $16$ , mean $16$ → mean $=$ median
D: median $17$ , mean $\approx17.14$ → mean $>$ median

Only Food Truck B has a median greater than its mean, so the correct answer is Food Truck B (choice B).

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation