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Answer
$Q_1=3.14$ Celsius, $M=6.4$ Celsius, $Q_3=9.75$ Celsius, $j=0.014$
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The following table shows data about monthly travelling expenses (in $f$) in a sample of $50$ local bus commuters.
$(1)$ Find the limits for the expense of central $50\%$ of the commuters.
$(2)$ Find the minimum expense of the highest spending $15\%$ commuters.
$(3)$ Find the maximum expense in the lowest spending $10\%$ commuters.
→$(1)$ Find the limits for the expense of central $50\%$ of the commuters.
$(2)$ Find the minimum expense of the highest spending $15\%$ commuters.
$(3)$ Find the maximum expense in the lowest spending $10\%$ commuters.
A producer believes that the mode of his daily production is $70.$ The distribution of production from the data obtained after making some changes in the design of the produced units is as follows :
Is there any change in the mode of the number of items produced ? .
→| No. of units | $60 – 64$ | $65- 69$ | $70 – 74$ | $75 – 79$ | $80 – 84$ | $85 – 89$ | $90 -94$ |
| No. of days | $5$ | $7$ | $10$ | $8$ | $5$ | $3$ | $2$ |
Out of $300$ persons residing in a region, a sample of $30$ persons is selected at random and the heights (in $cm$.) of these selected persons are as under :
$\text{163 148 151 162 145 152 149 158 153 149 150 152 145 141 162 168 148 158 149 141 146 155 159 150 161 153 162 160 154 165}$
$(i)$ Distribute these data into $6$ classes and also find the mid value of each class.
$(ii)$ Obtain ‘less than’ type cumulative frequency distribution.
$(iii)$ What is the percentage of persons having height less than $155 \ cm.$?
$(iv)$ Obtain ‘more than’ type cumulative frequency distribution.
$(v)$ How many persons have the height between $147$ to $157 \ cm.$?
→$\text{163 148 151 162 145 152 149 158 153 149 150 152 145 141 162 168 148 158 149 141 146 155 159 150 161 153 162 160 154 165}$
$(i)$ Distribute these data into $6$ classes and also find the mid value of each class.
$(ii)$ Obtain ‘less than’ type cumulative frequency distribution.
$(iii)$ What is the percentage of persons having height less than $155 \ cm.$?
$(iv)$ Obtain ‘more than’ type cumulative frequency distribution.
$(v)$ How many persons have the height between $147$ to $157 \ cm.$?
The observations of a data are obtained as follows. Prepare a frequency distribution using these data such that class length is $5$ and one of the classes is $30-34$.
$33,35,37,35,34,36,45,42,37,35,34,33,45,46,37,20,21$, $46,44,45,29,27,28,26,54,47,22,33,32,32,41,41,23,31$, $41,23,21,39,23,33,42,41,33,38,36,40,36,38,24,27 .$
→$33,35,37,35,34,36,45,42,37,35,34,33,45,46,37,20,21$, $46,44,45,29,27,28,26,54,47,22,33,32,32,41,41,23,31$, $41,23,21,39,23,33,42,41,33,38,36,40,36,38,24,27 .$
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 ).
$\text{13.25,14.20,13.75,14.10,14.00,12.85,13.40,14.20,15.30$, $15.40,16.10,15.80,15.60,15.10,14.85,14.75,15.25,16.45}$, $\text{16.40,16.55,17.10,16.90,16.80,17.00,16.40,16.50,16.60$, $16.65,16.70,16.85,17.00,17.25,17.50,17.45,17.60,17.75}$, $\text{17.40,17.35,17.45,17.50,17.60,17.50,17.65,17.25,18.10$, $17.00,17.20,17.50,17.80,17.90 .}$
→$\text{13.25,14.20,13.75,14.10,14.00,12.85,13.40,14.20,15.30$, $15.40,16.10,15.80,15.60,15.10,14.85,14.75,15.25,16.45}$, $\text{16.40,16.55,17.10,16.90,16.80,17.00,16.40,16.50,16.60$, $16.65,16.70,16.85,17.00,17.25,17.50,17.45,17.60,17.75}$, $\text{17.40,17.35,17.45,17.50,17.60,17.50,17.65,17.25,18.10$, $17.00,17.20,17.50,17.80,17.90 .}$
Owner of a factory has decided to Produce $50$ mixers used as household equipment, but the daily production of mixers changes due to variation in the number of workers. A variation in production of mixers with respect to a pre-decided number of Production ($100$ units) during $40$ days is recorded as under. Prepare an exclusive continuous frequency distribution having class length 6 and mid value of one of the classes as $3$. Also prepare ‘less than’ and ‘more than’ cumulative frequency distributions.
→The information regarding the production (in lakh ?) and sales (in lakh $T$) for a factory during five years is given below. Present it in a suitable diagram.
→The information of number of roses on $30$ rose plants in a nursery is given below. Find range, coefficient of range, quartile deviation, coefficient of quartile deviation, mean deviation and coefficient of mean deviation of the number of roses from it.
→In $100$ different days during a year, minimum $20$ and maximum $149$ pilgrims visited a religious place. Its frequency distribution is as follows. Find the coefficient of skewness using Bowley's method by preparing an inclusive frequency distribution taking class length $10$ for the first class.
→| No. of pilgrims (less than) | $29$ | $49$ | $69$ | $99$ | $129$ | $149$ |
| No. of days | $8$ | $21$ | $48$ | $75$ | $90$ | $100$ |
The marks obtained by two students $A$ and $B$ in $10$ sets of examinations are given below :
Which student is more consistent in his study?
→| Set | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
| Marks of $A$ | $44$ | $80$ | $76$ | $48$ | $52$ | $72$ | $68$ | $56$ | $60$ | $64$ |
| Marks of $B$ | $48$ | $75$ | $54$ | $60$ | $63$ | $69$ | $72$ | $51$ | $57$ | $56$ |