9th Maths 14.4
Exercise 14.4
Q1. The following number of goals were scored by a team in a series of `10` matches
`2, 3, 4, 5, 0, 1, 3, 3, 4, 3`
Find the mean, median, and mode of these scores.
Sol. :
By arranging the data in ascending order,
`0, 1, 2, 3, 3, 3, 3, 4, 4, 5.`
Mean `overlinex=(x_1+x_2+x_3+...+x_10)/10`
`(sum_(i=1)^10x_i)/n`
`= (0+1+2+3+3+3+3+4+4+5)/10`
`= 28/10`
So, `=2.8`
Median`=((n/2)^(th)term+(n/2+1)^(th)term)/2`
`=((10/2)^(th)term+(10/2+1)^(th)term)/2`
`=(5^(th)term+6^(th)term)/2`
`=(3+3)/2=6/2=3`
Mode`=`Maximum frequency`=3`
Answer:
Mean `=2.8`
Median `=3`
Mode `=3`
Q2. In a mathematics test given to `15` students, the following marks (out of `100`) are recorded:
`41, 39, 48, 52, 46, 54, 40, 96, 52, 98, 40, 42, 52, 60`
Find the mean, median, and mode of this data.
Sol. :
By arranging the data in ascending order
`39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54,` `60,` `62,` `96,` `98`
Mean `overlinex=(sum_(i=1)^nx_i)/n=(sum_(i=1)^(15)x_i)/15`
`=(39+40+40+41+42+46+48+52+52)/15`+`(54+60+62+96+98)/15`
`=822/15`
`=54.8`
Median`=((n+1)/2)^(th)term`
`=((15+1)/2)^(th)term`
`=8^(th)term=52`
Mode`=`Maximum frequency`=52`
Answer:
Mean`=54.8`
Median`=52`
Mode`=52`
Q3. The following observations have been arranged in ascending order. If the median of the data is `63`, find the value of `x`
`29, 32, 48, 50, x, , x+2, 72, 78, 84, 95`
Sol:
Median`=((n/2)^(th)term+(n/2+1)^(th)term)/2`
`63=(5^(th)term+6^(th)term)/2`
`63=(x+x+2)/2`
`63=(2x+2)/2`
`63times2=2x+2`
`126-2=2x`
`x=124/2`
`x=62`
Answer:
The value of `x=62`.
Q4. Find the mode of `14, 25, 14, 28, 18, 14, 23, 22, 14, 18.`
Sol. :
By arranging the data in ascending order
`14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28`
Mode`=`Maximum frequency`=14`
Answer:
Mode`=14`
Q5. Find the mean salary of `60` workers of a factory from the following table:
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Sol. :
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`f_ix_i` |
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Mean `overlinex=(sum_(i=1)^nf_ix_i)/n`
`overlinex=305000/60`
`overlinex= ₹ 5083.33`
Answer:
The mean salary of `60` workers is `₹ 5083.33`.
Q6. Give one example of a situation in which.
i) the mean is an approximate measure of central tendency.
ii) the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.
Sol. :
Example:
Mary and Hari received their test copies. The test had five questions, each carrying ten marks. their scores were as follows:
Hari's score |
i) Mary
Mean `overlinex=(sum_(i=1)^n)/n`
`=(sum_(i=1)^5)/5`
`=(10+8+9+8+7)/5`
`=42/5`
`=8.4`
Hari
Mean `overlinex=(sum_(i=1)^n)/n`
`=(sum_(i=1)^5)/5`
`=(4+7+10+10+10)/5`
`=41/5`
`=8.2`
Answer:
Mary's score better than Hari.
ii) By arranging the data in ascending order
Marry
`7, 8, 8, 9, 10`
Median`=3^(rd)term=8`
Harri
`4, 7, 10, 10, 10`
Median`=3^(rd)term=10`
Answer:
Hari's score better than Marry.
This comparison helps us in stating that these measures of central tendency are not sufficient for concluding which student is better. We require some more information to conclude this, which you will study about in the higher classes.
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