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Answer
Coefficient of Variation $=50.98 \%$
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The information of daily wages (in $Rs.$) of $230$ workers of a factory is given below. Calculate the coefficient of variation from the following data for the daily wages of workers :
→| Daily wages $(Rs)$ | No. of workers |
| Less than $100$ | $12$ |
| Less than $200$ | $30$ |
| Less than $300$ | $65$ |
| Less than $400$ | $107$ |
| Less than $500$ | $157$ |
| Less than $600$ | $202$ |
| Less than $700$ | $222$ |
| Less than $800$ | $230$ |
A transport company has $100$ trucks. These trucks are inspected for maintenance purpose and the following distribution is obtained for the number of defects in the trucks.
Find the range, coefficient of range, quartile deviation, mean deviation and coefficient of mean deviation for the number of defects per truck.
→| No. of Defects | $0$ | $1$ | $2$ | $3-4$ | $5-8$ | $9-14$ | $15-25$ |
| No. of trucks | $8$ | $12$ | $18$ | $24$ | $18$ | $12$ | $8$ |
Find the range, coefficient of range, quartile deviation, mean deviation and coefficient of mean deviation for the number of defects per truck.
A factory has $100$ machines for production. The following data are obtained about rejected items during the production process. Find the skewness and its coefficient using Karl Pearson’s method from these data.
→The data on retail price of a commodity for $50$ days are as follows. Classify the data iaking class length $1$ and the mid value of initial class $12.5$ into an appropriate continuous frequency distribution. (Price is per $kg$ in ).
$\text{13.25,14.20,13.75,14.10,14.00,12.85,13.40,14.20,15.30$, $15.40,16.10,15.80,15.60,15.10,14.85,14.75,15.25,16.45}$, $\text{16.40,16.55,17.10,16.90,16.80,17.00,16.40,16.50,16.60$, $16.65,16.70,16.85,17.00,17.25,17.50,17.45,17.60,17.75}$, $\text{17.40,17.35,17.45,17.50,17.60,17.50,17.65,17.25,18.10$, $17.00,17.20,17.50,17.80,17.90 .}$
→$\text{13.25,14.20,13.75,14.10,14.00,12.85,13.40,14.20,15.30$, $15.40,16.10,15.80,15.60,15.10,14.85,14.75,15.25,16.45}$, $\text{16.40,16.55,17.10,16.90,16.80,17.00,16.40,16.50,16.60$, $16.65,16.70,16.85,17.00,17.25,17.50,17.45,17.60,17.75}$, $\text{17.40,17.35,17.45,17.50,17.60,17.50,17.65,17.25,18.10$, $17.00,17.20,17.50,17.80,17.90 .}$
The earning of a shopkeeper (in complete rupees) for $30$ days are as under. Taking the initialclass $8000-8099$, prepare a frequency distribution.
$8200,8370,8180,8425,9030,8075,8700,8520,8875$, $8699,8280,8100,8368,8545,8785,8199,8435,9000,8650$, $8380,8075,8600,8760,8825,8990,9050,8340,8180$, $8290,8585 .$
→$8200,8370,8180,8425,9030,8075,8700,8520,8875$, $8699,8280,8100,8368,8545,8785,8199,8435,9000,8650$, $8380,8075,8600,8760,8825,8990,9050,8340,8180$, $8290,8585 .$
$20$ workers of a factory get bonus from $₹ 1000$ to $₹ 5000$ as per their performance. Its distribution is as follows.
Obtain coefficient of range, quartile deviation and standard deviation for the bonus.
→| Bonus (₹) | $1000$ | $2000$ | $3000$ | $4000$ | $5000$ |
| No. of workers | $3$ | $5$ | $6$ | $4$ | $2$ |
Obtain coefficient of range, quartile deviation and standard deviation for the bonus.
From the following data of runs scored by two batsmen $A$ and $B$ in last $10$ innings, decide who is more consistent.
→The height (in $\mathrm{cm}$ ) of nine pilots of Airforce are as follows:
$175,170,172,185,180,170,183,175,168 .$
Find the percentage of pilots whose heights are in the range $\bar{x} \pm S$.
→$175,170,172,185,180,170,183,175,168 .$
Find the percentage of pilots whose heights are in the range $\bar{x} \pm S$.
The following is a distribution of closing prices (in $Rs.$) of shares of $100$ different small scale industries on a certain day. Find the mean deviation of the closing prices of shares.
→| Price $(Rs.)$ | $0 – 10$ | $10 – 20$ | $20 – 30$ | $30 – 40$ | $40 – 50$ | $50 – 60$ | $60 – 70$ | $70 – 80$ | $80 - 90$ |
| No.of industries | $3$ | $8$ | $15$ | $20$ | $25$ | $10$ | $9$ | $6$ | $4$ |