Question

The frequency table below records the number of used cars sold (by price ranges) by one dealer back in 2019.

Price of car sold	Frequencies
0-4,999	11
5,000-9,999	28
10,000-14,999	23
15,000-19,999	8
20,000-24,999	5

Use your calculator to compute estimates for the following descriptive statistics for this sample of car prices sold by this dealer in 2019. Round answers on (a) to (e) to the nearest whole number with dimensional units included.

(a) Mean price:

(b) Median price:

(c) Standard Deviation of prices:

(d) Range of prices:

(e) Sample size:

7. Compute the relative frequency (to nearest 0.1%) for the class in #5 above that includes a car that sold for $7398.

Answer 1

(a) Mean Price:

=10366.1667

(b) Median Price:

o find Median Class
= value of ()th observation
= value of ()th observation
= value of 37th observation

From the column of cumulative frequency cf, we find that the 37th observation lies in the class 5000-9999.
The median class is 4999.5-9999.5.

Now,
L = lower boundary point of median class = 4999.5
n = Total frequency = 75
cf = Cumulative frequency of the class preceding the median class = 11
f = Frequency of the median class =28
c = class length of median class = 5000

Median

= 9731.6429

(c) Standard deviation:

= 5401.0343

(d) Range of Prices

= 24999 - 0

= 24999.

(e) Sample size (No. of observations) can be obtained by summing the frequencies

= 11 + 28 + 23 + 8 + 5 = 75

n = 75

7. The relative frequency (to nearest 0.1%) for the class in #5 above that includes a car that sold for $7398

The relative frequency of each class is the proportion of the data that falls in that class. Here, the required class is the one that includes the value $7398 i.e class (5,000-9,999)

Relative frequency

= 0.373