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Answer
$\bar{x}=37.5$ Marks, $M_0=36.42$ Marks, $s=16.5$ Marks, $j=0.07$
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Find the percentage of observations lying within the limits $x ± s$ using the following distribution of credit days taken by the merchants:
→| Credit days | $12$ | $13$ | $14$ | $15$ | $16$ | $17$ | $18$ | $19$ |
| No. of merchants | $5$ | $10$ | $25$ | $65$ | $45$ | $35$ | $8$ | $7$ |
The frequency distribution of hourly wages paid to $600$ workers is given below. Find the Karl Pearson’s coefficient of skewness from this distribution.
→The data of retail price (in $₹$) of an item for $40$ days are as follows. Prepare an inclusive frequency distribution having classlength 1 and one class $19-19.99$.
$\text{20.75 21.30 20.50 18.20 17.00 17.65 18.70 21.87}$
$\text{19.40 21.30 18.35 22.45 23.15 22.95 22.18 20.26}$
$\text{22.25 23.43 24.20 23.80 23.50 23.60 24.80 24.10}$
$\text{23.45 23.56 23.95 23.00 23.80 24.30 24.52 18.65}$
$\text{18.40 17.42 18.10 23.60 18.65 24.35 24.15 22.18}$
→$\text{20.75 21.30 20.50 18.20 17.00 17.65 18.70 21.87}$
$\text{19.40 21.30 18.35 22.45 23.15 22.95 22.18 20.26}$
$\text{22.25 23.43 24.20 23.80 23.50 23.60 24.80 24.10}$
$\text{23.45 23.56 23.95 23.00 23.80 24.30 24.52 18.65}$
$\text{18.40 17.42 18.10 23.60 18.65 24.35 24.15 22.18}$
The data related to variations in the price of a share for $30$ days in a share market are as under. Prepare an exclusive continuous of one of classification having class limits the classes as $18.5-20.5$.
$10.50,14.70,17.20,15.20,19.20,15.80,19.30$, $18.40,18.70,14.90,18.50,16.90,12.50,13.60,12.50$, $18.50,14.00,16.20,13.30,3.30,17.6020 .2014 .50$, $20.80,14.50,20.50,10.50,18.60,18.60,14.90$
On the basis of this frequency distribution, answer the following questions:
$(1)$ What is mid value of the 4 th class?
$(2)$ Find the number of days during which the price of share is at the most $Rs. 16.50$.
$(3)$ Find the number of days during which the price of share is at least $Rs. 19.50$.
→$10.50,14.70,17.20,15.20,19.20,15.80,19.30$, $18.40,18.70,14.90,18.50,16.90,12.50,13.60,12.50$, $18.50,14.00,16.20,13.30,3.30,17.6020 .2014 .50$, $20.80,14.50,20.50,10.50,18.60,18.60,14.90$
On the basis of this frequency distribution, answer the following questions:
$(1)$ What is mid value of the 4 th class?
$(2)$ Find the number of days during which the price of share is at the most $Rs. 16.50$.
$(3)$ Find the number of days during which the price of share is at least $Rs. 19.50$.
Discrete frequency distribution showing the number of children in $50$ families The data regarding the number of children of $50$ families residing in a certain area are given below. Prepare an appropriate frequency distribution.
$1, 1, 2, 1, 1, 1, 1, 2, 1, 0,$
$0, 2, 2, 0, 3, 3, 2, 1, 2, 1,$
$2, 1, 3, 1, 1, 2, 2, 2, 1, 2,$
$3, 0, 3, 0, 2, 1, 2, 3, 3, 2, 1,$
→$1, 1, 2, 1, 1, 1, 1, 2, 1, 0,$
$0, 2, 2, 0, 3, 3, 2, 1, 2, 1,$
$2, 1, 3, 1, 1, 2, 2, 2, 1, 2,$
$3, 0, 3, 0, 2, 1, 2, 3, 3, 2, 1,$
The area of $50$ fields (in hectares) is as follows. Prepare an appropriate frequency distribution.
$1.9,2.1,4.2,6.8,8.7,5.7,6.8,9.7,8.3,3.8,2.3,4.1,1.2,3.2$, $4.9,9.8,1.5,6.5,4.9,2.4,2.8,1.2,1.3,3.2,2.8,5.2,7.5,2.5$, $8.7,6.2,3.5,1.6,7.3,1.9,4.2,1.4,6.4,4.5,2.7,5.7,1.6$, $3.8,1.5,1.6,3.2,1.7,4.6,3.8,5.5,6.5 .$
→$1.9,2.1,4.2,6.8,8.7,5.7,6.8,9.7,8.3,3.8,2.3,4.1,1.2,3.2$, $4.9,9.8,1.5,6.5,4.9,2.4,2.8,1.2,1.3,3.2,2.8,5.2,7.5,2.5$, $8.7,6.2,3.5,1.6,7.3,1.9,4.2,1.4,6.4,4.5,2.7,5.7,1.6$, $3.8,1.5,1.6,3.2,1.7,4.6,3.8,5.5,6.5 .$
In a university, out of total $50,000$ students, $35\%$ are in commerce faculty, $30\%$ are in arts faculty, $20\%$ are in science faculty, $10\%$ are in engineering faculty and remain- ing $5$"/u are in medical faculty. The ratio of number of boys and girls in commerce faculty is $4:3$. ln arts faculty, the number of girls is double than that of boys. In science and engineering faculty, there are $60\%$ and $70\%$ boys respectively and in medical faculty, boys and girls are in equal numbers.
→The following table gives ages of $80$ students selected from a college.
→|
Age (years)
|
$17$ | $18$ | $19$ | $20$ | $21$ | $22$ | $23$ |
|
No. of students
|
$11$ | $14$ | $22$ | $15$ | $8$ | $6$ | $4$ |
Find median age. Also find $Q1,DA,P32$ for age and interpret them.
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 ).
$\text{13.25,14.20,13.75,14.10,14.00,12.85,13.40,14.20,15.30$, $15.40,16.10,15.80,15.60,15.10,14.85,14.75,15.25,16.45}$, $\text{16.40,16.55,17.10,16.90,16.80,17.00,16.40,16.50,16.60$, $16.65,16.70,16.85,17.00,17.25,17.50,17.45,17.60,17.75}$, $\text{17.40,17.35,17.45,17.50,17.60,17.50,17.65,17.25,18.10$, $17.00,17.20,17.50,17.80,17.90 .}$
→$\text{13.25,14.20,13.75,14.10,14.00,12.85,13.40,14.20,15.30$, $15.40,16.10,15.80,15.60,15.10,14.85,14.75,15.25,16.45}$, $\text{16.40,16.55,17.10,16.90,16.80,17.00,16.40,16.50,16.60$, $16.65,16.70,16.85,17.00,17.25,17.50,17.45,17.60,17.75}$, $\text{17.40,17.35,17.45,17.50,17.60,17.50,17.65,17.25,18.10$, $17.00,17.20,17.50,17.80,17.90 .}$