Question

Mouse weights. Find the mean and median for the data in the following table.

Interval	41.5minus−43.5	43.5minus−45.5	45.5minus−47.5	47.5minus−49.5	49.5minus−51.5	51.5minus−53.5	53.5minus−55.5	55.5minus−57.5	57.5minus−59.5
Frequency	44	55	1414	1515	2020	1515	1717	77	22

meanequals=50.5850.58

​(Round to two decimal places if​ needed.)

medianequals=??

​(Round to two decimal places if​ needed.)

Answer 1

Mouse weights. Find the mean and median for the data in the following table.

Interval	41.5−43.5	43.5−45.5	45.5−47.5	47.5−49.5	49.5−51.5	51.5−53.5	53.5−55.5	55.5−57.5	57.5−59.5
Frequency	4	5	14	15	20	15	17	7	2

mid-point = (lower limit + upper limit)/2

Mid-Point(x)	42.5	44.5	46.5	48.5	50.5	52.5	54.5	56.5	58.5
Frequency (f)	4	5	14	15	20	15	17	7	2

= 4 + 5 + 14 + 15 + 20 + 15 + 17 + 7 + 2 = 99

Mean =

= (4 * 42.5 + 5 * 44.5 + 14 * 46.5 + 15 * 48.5 + 20 * 50.5 + 15 * 52.5 + 17 * 54.5 + 7 * 56.5 + 2 * 58.5) / 99

= 50.58

Interval	41.5−43.5	43.5−45.5	45.5−47.5	47.5−49.5	49.5−51.5	51.5−53.5	53.5−55.5	55.5−57.5	57.5−59.5
Cumulative Frequency (f)	4	9	23	38	58	73	90	97	99

For sample size of 99, the median will be (99 + 1)/2 = 50th data value.

From the cumulative frequency, the median lies in the interval 49.5−51.5

Estimated Median = L + [((n/2) − B) / G] × w

where:

• L is the lower class boundary of the group containing the median
• n is the total number of values
• B is the cumulative frequency of the groups before the median group
• G is the frequency of the median group
• w is the group width

L = 49.5, n = 99, B = 38 , G = 20, w = 2

Estimated Median = 49.5 + [((99/2) − 38) / 20] × 2

= 50.65