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We all know that fruit is good for us. Below is a histogram of the number of servings of fruit per day claimed by 74seventeen-year-old girls in a study in Pennsylvania?

(a) With a little care, you can find the median and the quartiles from the histogram. What are these numbers? How did you find them?

(b) Estimate the mean of the distribution. Explain your method clearly.

Short Answer

Expert verified

Part(a) Median 74

Q1=1Q3=4

Part (b)X2.59

Step by step solution

01

Part (a) Step 1: Given information

Given graph :

02

Part (a) Step 2: Concept

The mean of a data set is determined by adding all of the numbers in the set and dividing by the number of values in the set. The median is the value in the middle of a data set when it is arranged from smallest to largest. The mode is the number that appears the most frequently in a data set.

03

Part (a) Step 3: Calculation

According to a study in Pennsylvania, the median amount of servings of fruit per day claimed by 74seventeen-year-old females is2, the first quartile is 1and the third quartile is 4To find the median and quartiles, use the formulas below:

Domain main lengthFrequency(f)Commulative frequency (Cf)
01515
11126
21541
31152
4860
5565
6368
7371
8374

The median can be calculated as follows:

M=N+12N=CumilativefrequencyM=74+12M=37.5thitem=2Q1=N+14thitemQ1=754thitemQ1=18.75thitem=1Q3=3(N+1)4thitem=3754thitem=56.25thitem=4

Therefore, the median is 2and the quartiles are 1and 4respectively.

04

Part (b) Step 1: Calculation

From the given histogram of number of servings of fruit per day claimed by 74 seventeen years old girls is a study in Pennsylvania the mean

Domain name length (X)Frequency (f)tx
0150
11111
21530
31133
4832
5525
6318
7321
8324

The mean of the distribution is X=fxf=19474X=2.59

Therefore, mean is 2.59

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