Solution Found!
The number of families who used the Minneapolis YWCA day
Chapter 2, Problem 52E(choose chapter or problem)
The number of families who used the Minneapolis YWCA day care service was recorded over a 30-day period. The results are as follows:
31, 49, 19, 62, 24, 45, 23, 51, 55, 60, 40, 35, 54, 26, 57, 37, 43, 65, 18, 41, 50, 56, 4, 54, 39, 52, 35, 51, 63 and 42.
a. Construct a cumulative frequency distribution of this data.
b. Sketch a graph of the cumulative frequency polygon.
c. How many days saw fewer than 30 families utilize the day care centre?
d. How busy were the highest 80 percent of the days?
Questions & Answers
QUESTION:
The number of families who used the Minneapolis YWCA day care service was recorded over a 30-day period. The results are as follows:
31, 49, 19, 62, 24, 45, 23, 51, 55, 60, 40, 35, 54, 26, 57, 37, 43, 65, 18, 41, 50, 56, 4, 54, 39, 52, 35, 51, 63 and 42.
a. Construct a cumulative frequency distribution of this data.
b. Sketch a graph of the cumulative frequency polygon.
c. How many days saw fewer than 30 families utilize the day care centre?
d. How busy were the highest 80 percent of the days?
ANSWER:Step 1 of 4
(a)
For 30 observations, determine the number of classes using the “2 to the k rule”:
\({2^4} = 16\)
16 is less than 30, so 4 classes is not enough.
Try the next highest number: \({2^5} = 32\)
32 is greater than 30, so the recommended number of classes is 5.
The class interval is given by:
\(i \ge \frac{{H - L}}{k}\)
Where i is the class interval, H is the highest observed value, L is the lowest observed value, and k is the number of classes.
Calculate class interval as,
\(\frac{{65 - 4}}{5} = 12.2\)
Round up to get a class interval of 15.
5 classes of width 15 results in a range of 75.
The actual range is,
65 – 4 = 61
Compare the two values:
75 – 61 = 14
Excess of 14.
The recommended lower limit is 4 – 4 = 0 (half of 14 is 7, but the lower limit should not be less than 0, and deducting 7 from the lowest observation of 4 would yield a negative number).
Organize classes based on class intervals and lower limits.
Count the number of units that fall into each class.
