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$M_{ o }=37.67$ Viewers
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From the following frequency distribution of different youngsters exercising in a gymnasium.
Find coefficient of skewness by Bowley’s method and state the type of skewness :
→Find coefficient of skewness by Bowley’s method and state the type of skewness :
| Age (years) | $25$ | $17$ | $20$ | $18$ | $26$ | $22$ | $28$ | $23$ |
| No. of youngsters | $22$ | $4$ | $19$ | $11$ | $7$ | $9$ | $3$ | $8$ |
There are respectively $60$ and $65$ students in two classes $A$ and $B$ of Std. $11$. The average marks in Statistics of both the classes are respectively $48.2$ and $54.4$. Find the average marks of all the students of Std. $11$ in the subject Statistics.
→The temperature (in Celsius) at a tourist place for $60$ days in the year $2014$ is as follows.
Using this information, find skewness and its coefficient by Karl Pearson's method. State the type of skewness.
→Using this information, find skewness and its coefficient by Karl Pearson's method. State the type of skewness.
|
Temperature (Celsius)
|
$-3^{\circ}$ to $-1^{\circ}$ | $-1^{\circ}$ to $5^{\circ}$ | $5^{\circ}$ to $11^{\circ}$ | $11^{\circ}$ to $19^{\circ}$ | $19^{\circ}$ to $23^{\circ}$ | $23^{\circ}$ to $27^{\circ}$ |
|
No. of days
|
$4$ | $14$ | $20$ | $14$ | $5$ | $3$ |
The frequency distribution of advertisement expenses (in thousand ₹) of $100$ companies is as follows. Find the coefficient of skewness by Bowley's method.
→| Advertisement expenses (thousand ₹) | $20-39.9$ | $40-59.9$ | $60-79.9$ | $80-99.9$ | $100-119.9$ |
| No. of companies | $18$ | $20$ | $23$ | $22$ | $17$ |
The information regarding the production (in lakh ?) in a factory during five years is given below. Present it in a suitable diagram.
Arrangements are made using all the letters of the word $\text{YOUNG}$. If all these arrangements are arranged in the order of dictionary, what will be the rank of the word $\text{YOUNG ?}$
→Marks obtained by $50$ students in a test of $50$ marks are as follows :
$\text{16 18 27 31 43 25 28 30 29 15}$
$\text{20 27 31 34 39 41 22 28 31 16}$
$\text{21 29 38 24 30 24 26 17 30 22}$
$\text{28 35 23 18 24 32 37 27 32 38}$
$\text{19 25 33 25 29 25 34 45 26 24}$
$(i)$ From these data, prepare a frequency distribution by taking class length $5$ .
$(ii)$ Obtain 'less than' and 'more than' type cumulative frequency distribution.
$(iii)$ If standard of passing is $20$ marks, then how many students have failed ?
$(iv)$ If at least $30$ marks are required to get first class, find the number of students in this category.
→$\text{16 18 27 31 43 25 28 30 29 15}$
$\text{20 27 31 34 39 41 22 28 31 16}$
$\text{21 29 38 24 30 24 26 17 30 22}$
$\text{28 35 23 18 24 32 37 27 32 38}$
$\text{19 25 33 25 29 25 34 45 26 24}$
$(i)$ From these data, prepare a frequency distribution by taking class length $5$ .
$(ii)$ Obtain 'less than' and 'more than' type cumulative frequency distribution.
$(iii)$ If standard of passing is $20$ marks, then how many students have failed ?
$(iv)$ If at least $30$ marks are required to get first class, find the number of students in this category.
The earning of a shopkeeper (in complete rupees) for $30$ days are as under. Taking the initialclass $8000-8099$, prepare a frequency distribution.
$8200,8370,8180,8425,9030,8075,8700,8520,8875$, $8699,8280,8100,8368,8545,8785,8199,8435,9000,8650$, $8380,8075,8600,8760,8825,8990,9050,8340,8180$, $8290,8585 .$
→$8200,8370,8180,8425,9030,8075,8700,8520,8875$, $8699,8280,8100,8368,8545,8785,8199,8435,9000,8650$, $8380,8075,8600,8760,8825,8990,9050,8340,8180$, $8290,8585 .$
The following table shows data about the distance travelled: (in km) by a salesman on different days. Find median, $Q_3, D_8, P_{62}$ and interpret them:
We obtain the cumulative frequency distribution for the given frequency distribution.
→| Distance travelled (km) | $0 – 100$ | $100 – 200$ | $200 – 300$ | $300 – 400$ | $400 – 500$ | $500 - 600$ |
| No. of days | $5$ | $18$ | $24$ | $7$ | $5$ | $1$ |
Following data are obtained for two groups $G_{1}$ and $G_{2}$ Find combined mean and combined standard deviation.
Group $G_{1}: n_{1}=20 ; \bar{x}_{1}=35 ; S_{1}^{2}=15$
Group $G_{2}: n_{2}=30 ; \bar{x}_{2}=40 ; S_{2}^{2}=12$
→Group $G_{1}: n_{1}=20 ; \bar{x}_{1}=35 ; S_{1}^{2}=15$
Group $G_{2}: n_{2}=30 ; \bar{x}_{2}=40 ; S_{2}^{2}=12$