Problem 52E

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 center?

d. How busy were the highest 80 percent of the days?

Problem 52E

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?

Step by step solution

Step 1 of 5

Given: The data of the number of families who used the Minneapolis YWCA day care service was recorded over a 30-day period is,

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. From the given data,

Maximum number of families = 65

Minimum number of families = 4

Range of number of families can be calculated as,

Number of classes can be computed as ‘k’ that satisfies . The value of k that satisfies the equation is . Let, number of classes (k) = 7 and width of interval = 10.

Cumulative Frequency Distribution of the data is tabulated as:

Class Interval |
Frequency |
Cumulative Frequency |

0-10 |
1 |
1 |

10-20 |
2 |
1+2 = 3 |

20-30 |
3 |
3+3 = 6 |

30-40 |
5 |
6+ 5 = 11 |

40-50 |
6 |
11+6 = 17 |

50-60 |
9 |
17+9 = 26 |

60-70 |
4 |
26+4 = 30 |