Chapter 1: Q 95. (page 75)

Do adolescent girls eat fruit? We all know that fruit is good for us. Here is a histogram of the number of servings of fruit per day claimed by 74 seventeen-year-old girls in a study in Pennsylvania:
(a) Find the median number of servings of fruit per day from the histogram. Explain your method clearly.
(b) Calculate the mean of the distribution. Show your work.

Short Answer

Expert verified

Part (a) 2 servings of fruit each day.

Part (b) Mean is approx 2.62servings of fruit per day.

Step by step solution

Part (a) Step 1. Given information.

The given histogram is shown below:

Part (a) Step 2. Find the median.

Servings of fruit per day	Frequency
0	15
1	11
2	15
3	11
4	8
5	5
6	3
7	3
8	3

As we know that median is the middle value of a data set. As the given set is even, the median will be the average of two middle values (37th and 38th) of this sorted data.

Because $15 + 11 = 26$ (sum frequencies first two bars) and $15 + 11 + 15 = 41$ (sum frequencies first three bars), the 37th and 38th data values are both equal to 2 in the histogram's third bar.

$M = \frac{2 + 2}{2} = 2$

The median units are the same as the data values' units, so the median is 2 servings of fruit each day.

Part (b) Step 1. Calculate the mean of the distribution.

$\bar{x} = \frac{\sum (f \cdot x)}{n} = \frac{(15 \times 0) + (11 \times 1) + (15 \times 2) + (11 \times 3) + (8 \times 4) + (5 \times 5) + (3 \times 6) + (3 \times 7) + (3 \times 8)}{15 + 11 + 15 + 11 + 8 + 5 + 3 + 3 + 3} = \frac{194}{74} \approx 2.6216$