# STATISTICS PROBLEMS WITH SOLUTIONS FOR GRADE 10

Statistics Problems with Solutions for Grade 10 :

Here we are going to see, some example problems in the topic statistics.

## Statistics Problems with Solutions for Grade 10

Question 1 :

The frequency distribution is given below.

In the table, k is a positive integer, has a variance of 160. Determine the value of k.

Solution :

Variance  =  (Σfd2/Σf) - (Σfd/Σf)2

d = x - A (A = 3k)

 xk2k3k4k5k6k f211111 d = x - A-2k-k0k2k3k fd-4k-k0k2k3k fd28k2k20k24k29k2

Σfd  =  -5k + k + 2k + 3k

Σfd  =  k

Σfd2  =  23k2 and Σf  =  7

Variance  =  (23k2/7) - (k/7)2

=  (161k2 - 1k2)/49

=  160k2/49

160k2/49  =  160

k2/49  =  1

k2  =  49

k = 7

Question 2 :

The standard deviation of some temperature data in degree celsius (oC) is 5. If the data were converted into degree Farenheit (oF) then what is the variance?

Solution :

Question 3 :

If for a distribution, Σ(x −5) = 3, Σ(x −5)2 = 43,and total number of observations is 18, find the mean and standard deviation

Solution :

Σ(x −5) = 3

Σx − Σ5 = 3

Σx − 18(5) = 3

Σx  = 90 + 3  ==>  93

Σ(x −5)2 = 43

Σ(x2 - 10x + 52) = 43

Σ(x2 - 10x + 25) = 43

Σx2 - 10Σx + 25Σ = 43

Σx2 - 10(93) + 25(18) = 43

Σx2  = 43 + 930 - 450

Σx2  = 523

Mean :

=  Σx/n  =  93/18  =  5.17

Standard deviation :

x2/n) -(Σx/n)2

=  √(523/18) - (5.17)2

=  √29.05 - 26.72

=  √2.33

S.D  =  1.53

Question 4 :

Prices of peanut packets in various places of two cities are given below. In which city, prices were more stable?

Solution :

By finding the coefficient of variation, we come to know that which is more stable.

Standard deviation :

σ  =  x2/n) -(Σx/n)2

## City A

 x2022192316------100 x2400484361529256------2030

## City B

 x1020181215------75 x2100400324144225------1193

For city A :

σ  =  x2/n) -(Σx/n)2

=  (2030/5) -(100/5)2

=  √406 - 400

=  √6

=  2.44

Coefficient of variation  =  (σ/x̄) x 100%

=  (2.44/20) x  100%

=  12.2

For city B :

σ  =  x2/n) -(Σx/n)2

=  (1193/5) -(75/5)2

=  √238.6 - 225

=  √13.6

=  3.68

Coefficient of variation  =  (σ/x̄) x 100%

=  (3.68/15) x  100%

=  24.53

Hence in city A, prices are more stable.

Question 5 :

If the range and coefficient of range of the data are 20 and 0.2 respectively, then find the largest and smallest values of the data.

Solution :

Range  =  L - S  =  20  ---(1)

Coefficient of range  =  (L - S)/(L + S)  =  0.2

20/(L + S)  =  0.2

L + S  =  20/0.2

L + S  =  100 ---(2)

(1) + (2)

2L  =  120

L  =  60

By applying the value of L, we get

S  =  100 - 60

S  =  40

Hence the largest and smallest values are 60 and 40 respectively.

After having gone through the stuff given above, we hope that the students would have understood, "Statistics Problems with Solutions for Grade 10".

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