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.