mean median histogram

Question

A sample of the daily earnings of a food vendor on a street was collected for 300 days. The distribution of earnings is as follows:

Earning range($): 100-200 200-250 250-300 300-400 400-600

No. of days: 40 60 50 70 80

i) On what percentage of the days did the vendor earn less than $270?

ii) Calculate mean and median of the distribution.

iii) Construct a histogram for the above data and comment on its symmetry.

Answer 1

ii) mean = sum (f * midpoint)/sum(f)

f midpoint f*midpoint

40 150 6000

60 225 13500

50 275 13750

70 350 24500

80 500 40000

--- ---------

300 97750

mean = 97750/300 = 325.83

median is group containing the 0.5 * (301) = 155.5th value (average of 155th and 156th value) which is in the 300-400 group

Median = L + ((n/2) - B)/G * w

where L is the lower class boundary of the group containing the median (300)

n is the total number of values (300)

B is the cumulative frequency of the groups before the median group (40+60+50 = 150)

G is the frequency of the median group (70)

w is the group width (100)

Median = 300 + ((300/2) - 150)/70 * 100 = 300