Statistics Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts
Statistics PRACTICE TEST [1 - EXERCISES]
Statistics Model Questions Set 1
Question : 26
Consider the following data:
| x | 1 | 2 | 3 | 4 | 5 |
| f | 3 | 5 | 9 | - | 2 |
a) 6
b) 7
c) 4
d) 8
Answer »Answer: (a)
| x | f | xf |
| 1 | 3 | 3 |
| 2 | 5 | 10 |
| 3 | 9 | 27 |
| 4 | $f_1$ | $4f_1$ |
| 5 | 2 | 10 |
| Total | 19 + $f_1$ | 50 + $4f_1$ |
∴ Mean = ${Σx_if_i}/{Σ_i}$
⇒ 2.96 = ${50 + 4f_1}/{19 + f_1}$ [given]
⇒ 56.24 + 2.96 $f_1 = 50 + 4f_1$
⇒ 6.24 = 1.04 $f_1$
⇒ $f_1$ = 6
Question : 27
What is the median of the data 3, 5, 9, 4, 6, 11, 18?
a) 6.5
b) 7
c) 6
d) 7.5
Answer »Answer: (c)
Arrange the number ascending order
3, 4, 5, 6, 9, 11, 18
Therefore $4^{th}$ term out of 7 is Median.
∴ Median = 6
Question : 28
A new frequency distribution is constructed by doubling each frequency of the original distribution keeping the other entries intact. The following measures are computed for both the tables:
I. Arithmetic mean
II. Median
III. Harmonic mean
Which of the following statements with reference to above is correct?
a) Corresponding values of I and III only are equal in both the distributions
b) Corresponding values of II and III only are equal in both the distributions
c) Corresponding values of I and II only are equal in both the distributions
d) Corresponding values of I, II and III are equal in both the distributions
Answer »Answer: (d)
If we double each value of original frequency distribution, then mean, median and harmonic mean remain same. Hence, option (d) is correct. Since, in case observation since arithmetic mean, median and harmonic mean is dependent of change of origin but if we multiply the frequency of same quantity, then, these are independent.
Question : 29
As the number of observations and classes increases, the shape of a frequency polygon
a) Tends to become increasingly smooth
b) Stay the same
c) Tends to become jagged
d) Varies only if data become more reliable
Answer »Answer: (a)
As the number of observations and classes increases, the shape of frequency polygon tends to become increasingly smooth.
Question : 30
Consider the following frequency distribution :
| Class | Frequency |
| 0-10 | 4 |
| 10-20 | 5 |
| 20-30 | 7 |
| 30-40 | 10 |
| 40-50 | 12 |
| 50-60 | 8 |
| 60-70 | 4 |
a) 40.66
b) 42.66
c) 38.33
d) 43.33
Answer »Answer: (d)
| Class | Mid values | Frequency $F_i$ | $d_I = x_i$ - 35 | $U_i = {x_1 - 35}/{10}$ | $f_I U_I$ | Cumulative Frequency |
| 0 - 10 | 5 | 4 | -30 | -3 | -12 | 4 |
| 10 - 20 | 15 | 5 | -20 | -2 | -10 | 9 |
| 20 - 30 | 25 | 7 | -10 | -1 | -7 | 16 |
| 30-40 | 35 | 10 | 0 | 0 | 0 | 26 |
| 40 - 50 | 45 | 12 | 10 | 1 | 12 | 38 |
| 50 - 60 | 55 | 8 | 20 | 2 | 16 | 46 |
| 60 - 70 | 65 | 4 | 30 | 3 | 12 | 50 |
$ΣF_iU_i = 11$
N = $Σf_i = 50$
$N/2 = {50}/2 = 25$
Mode = $l + {f - f_1}/{2f - f_1 - f_2} × h$
Here, the maximum frequency is 12 their class is
40 – 50, then l = 40 f = 12, $f_1 = 10, f_2$ = 8
mode = 40 + ${12 - 10}/{2 × 12 - 10 - 8}$ × 10
= 40 + $2/6$ × 10 = 40 + 3.33 = 43.33
IMPORTANT quantitative aptitude EXERCISES
Statistics Model Questions Set 1 Online Quiz
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