Construct a continuous frequency distribution for the following heights (in cm) of 50
students in a class and draw its frequency polygon:
146 156 152 167 178 180 172 162 148
153 161 173 163 174 147 179 148 151
168 172 165 173 172 180 175 145 153
154 162 164 170 172 160 161 158 152
163 165 170 168 158 149 155 160 150
149 167 176 169 159
The continuous frequency distribution for the given
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State whether the following statements are true or false. Give brief justification.
a) The number of samples of size 3 with replacement from a population of size 6 is 20.
b) If the odds in favour of an event A are 3 : 4, then the probability of occurrence of A
will be 4/7.
c) If the level of significance is the same, the area of the rejection region in a 2-tailed
test is less than that in a 1-tailed test.
d) There is no seasonal variation in an annual time series.
e) In a binomial distribution, if X represents the number of successes in 25 trials and the
probability of success at each trial is 0.5, then the standard deviation of X is 2.
In a partially destroyed laboratory record of an analysis of correlation data, the
following results are legible:
The equations of two regression lines are as follows:
3Y 9X 46
3X 12Y 19
 
 
Obtain (i) mean values of X and Y; (ii) the values of regression coefficients; and (iii)
the value of correlation coefficient.
A company appointed four salesman A, B, C and D and observed their sales in three
seasons – Summer, Winter and Monsoon. Test whether the average sales of the four
salesmen differ in amount (in Rs. Lakhs) as given below by one-way analysis of
variance (ANOVA) using observations after taking deviation from 30.
Two sets of ten students selected at random from a college were taken; one was given memory test as they were and the other set was given a memory test after two weeks’ training and the scores are given below:
| Set A | Set B |
| 10 | 12 |
| 8 | 8 |
| 7 | 8 |
| 9 | 10 |
| 8 | 8 |
| 10 | 11 |
| 9 | 9 |
| 6 | 8 |
| 7 | 9 |
| 8 | 9 |
A hospital has 25 centres located at different places in a state. Each centre has been provided with 4 paramedics. In order to estimate the average number of patients handled by a paramedic on a typical day at a centre, a sample of 5 centres was selected, using without replacement simple random sampling. The data regarding the number of patients on a typical working day for each selected centre are given below:
| Centre | m | Patients seen | |||
| 1 | 4 | 1 | 2 | 6 | 3 |
| 2 | 4 | 4 | 3 | 2 | 2 |
| 3 | 4 | 5 | 3 | 2 | 1 |
| 4 | 4 | 4 | 1 | 5 | 6 |
| 5 | 4 | 2 | 3 | 4 | 7 |
1000 students at college level were graded according to their IQ levels and the economic condition of their parents, as follow:
| Economic condition | IQ level | ||
| High | Low | Total | |
| Rich | 230 | 170 | 400 |
| Poor | 230 | 130 | 600 |
|
Total | 700 | 300 | 1000 |
The frequency distribution of marks of 230 students in a statistics paper in a class is given below:
Class Interval Frequency
10 – 20 12
20 – 30 30
30 – 40 ?
40 – 50 65
50 – 60 ?
60 – 70 25
70 – 80 18
Total 230
Given that the median value of distribution is 46, determine the missing frequencies.