Researchers collected data on calories per serving for 77 brands of breakfast cereal. The histogram displays the data 30

25-

20

1

Frequency

15

What is the approximate center of this distribution?

The center of the distribution is between 120 and 130

calories.

The center of the distribution is between 90 and 100

calories.

The center of the distribution is between 110 and 120

calories.

The center of the distribution is between 80 and

90 calories.

The center of the distribution is between 130 and 140

calories.

10

-

50 60 70 80 90 100 110 120 130 140 150 160

Calories

Histogram attached

Answer and explanation:

To find the center of the distribution, we find the mean of the distribution.

Mean= sum of all values/number of values

To calculate the mean of the distribution using the histogram(attached) with given frequencies, we find the mid point of each class and multiply by its frequency to get the sum of the values(estimated) and then divide by the number of values(sum of the frequencies of the classes)

midpoint of 50-60=50+60/2=55

midpoint of 70-80=150/2= 75

midpoint of 80-90=170/2=85

midpoint of 90-100=190/2=95

midpoint of 100-110=210/2=105

Midpoint of 110-120=230/2=115

Midpoint of 120-130=250/2=125

Midpoint of 130-140=270/2=135

Midpoint of 140-150=290/2=145

Midpoint of 150-160=310/2=155

Sum of the values= 55*frequency= 55*3+75* 2+85*1+95*7+105*17+115*29+125*10+

135*2+145*3+155*3

Sum of all values =8605

Number of values= 3+2+1+7+17+29+10+2+3+3=77

Mean= 8605/77= 111.753

Therefore the center of the distribution is between 110 and 120 calories.

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