Question

construct the cumulative - frequency distribution for the given data.
daily low (°f)\t35 - 39\t40 - 44\t45 - 49\t50 - 54\t55 - 59\t60 - 64\t65 - 69
frequency\t3\t2\t5\t14\t8\t6\t1
daily low temperature (°f)\tless than 40\tless than 45\tless than 50\tless than 55\tless than 60\tless than 65\tless than 70
cumulative frequency

Explanation:

Step1: Initialize cumulative frequency

The cumulative frequency for values less than 40 is the frequency of the 35 - 39 class. So, for "Less than 40", cumulative frequency = 3.

Step2: Calculate cumulative frequency for less than 45

Add the frequency of the 40 - 44 class to the previous cumulative frequency. Cumulative frequency for "Less than 45" = 3+2 = 5.

Step3: Calculate cumulative frequency for less than 50

Add the frequency of the 45 - 49 class to the previous cumulative frequency. Cumulative frequency for "Less than 50" = 5 + 5=10.

Step4: Calculate cumulative frequency for less than 55

Add the frequency of the 50 - 54 class to the previous cumulative frequency. Cumulative frequency for "Less than 55" = 10+14 = 24.

Step5: Calculate cumulative frequency for less than 60

Add the frequency of the 55 - 59 class to the previous cumulative frequency. Cumulative frequency for "Less than 60" = 24+8 = 32.

Step6: Calculate cumulative frequency for less than 65

Add the frequency of the 60 - 64 class to the previous cumulative frequency. Cumulative frequency for "Less than 65" = 32+6 = 38.

Step7: Calculate cumulative frequency for less than 70

Add the frequency of the 65 - 69 class to the previous cumulative frequency. Cumulative frequency for "Less than 70" = 38+1 = 39.

Answer:

Daily Low Temperature ($^{\circ}$F)	Cumulative Frequency
Less than 45	5
Less than 50	10
Less than 55	24
Less than 60	32
Less than 65	38
Less than 70	39