Question

The frequency distribution shows the number of registered motor vehicles for a random sample of 200 California households.

(a) Find the mean number of registered vehicles per California household.
Answer:
____vehicles
(b) Find the median number of registered vehicles per California household.
Answer:
___vehicles

Answer 1

1). Mean = 2.275

2). Median = 2 vehicles

Explanation:

From the given table,

Number of vehicles (x) Frequency (f) (f)×(x) Cumulative freq.

0 11 0 11

1 52 52 63

2 66 132 129

3 35 105 164

4 19 76 183

5 12 60 195

6 5 30 200

`\sum (f* x) = 455`

Number of households = 200

Mean =
`\sum (f.x)/(n)`

=
`(455)/(200)`

= 2.275

Median = value of
`((n+1))/(2)th` observation

= value of
`(201)/(2)th` observation

= Value of 100.5th observation

= Since 100.5th observation lies in the row of cumulative freq. = 129

= 2

Therefore, median number of registered vehicles per California household

= 2 vehicles