HYRIGH fararefant et fanter i In a class of 25 student,
1 answer:
Given:
Total students in a class = 25
Students who like volleyball = 17
Students who like basketball = 15
Students who like both = 10
To find:
The students who don't like any of the games.
Solution:
We have,
Total students in a class = 25
Students who like volleyball = 17
Students who like basketball = 15
Students who like both = 10
Now,
Students who like only volleyball = 17-10
= 7
Students who like only basketball = 15-10
= 5
Students who don't like any of the games is the difference of total number of students and number of students who like at least one game.
Students who don't like any of the games = 25 - (7+5+10)
= 25 - 22
= 3
Therefore, 3 students don't like any of the games.
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The obtained answers for the given frequency distribution are:
(a) The formula for the mean in sigma notation is where n is the number of observations;
are the n observations.
The mean for the given monthly plan price is $16.1.
(b) The frequency distribution for given data is {$9.99 - 2; $10 - 5; $12 - 1; $12.75 - 2; $14.99 - 6; $20 - 4; $25 - 5}
(c) The formula for the mean using the frequency distribution table is where
and on applying this formula for the given data, the mean is $16.1.
(d) The median for the given data is , and the mode for the given data is $14.99
The frequency distribution has sample observations and frequencies
.
Then, the mean is calculated by
Where (Sum of frequencies)
The median is calculated by
The mode is calculated by
Mode = highest frequency value
<h3>Calculation:</h3>The given list of data is
{$14.99, $12.75, $14.99, $14.99, $9.99, $25, $25, $10, $14.99, $10, $20, $10, $20, $14.99, $10, $25, $20, $12, $14.99, $25, $25, $20, $12.75, $10, $9.99}
(a) Formula for the mean using sigma notation and use it to calculate the mean:
The formula for the mean is
Where n = 25; - n observations
On substituting,
Mean
=1/25(14.99+12.75+14.99+14.99+9.99+25+25+10+14.99+10+20+10+20+14.99+10+25+20+12+14.99+25+25+20+12.75+10+9.99)
= 1/25(402.42)
= 16.09 ≅ 16.1
(b) Constructing a frequency distribution for the data:
Cost - frequency - cumulative frequency
$9.99 - 2 - 2
$10 - 5 - 7
$12 - 1 - 8
$12.75 - 2 - 10
$14.99 - 6 - 16
$20 - 4 - 20
$25 - 5 - 25
Sum of frequencies N = 25;
(c) Using frequency distribution, calculating the mean:
The formula for finding the mean using frequency distribution is
Where N = 25;
On substituting,
<em> </em>= 1/25 (2 × 9.99 + 5 × 10 + 1 × 12 + 2 × 12.75 + 6 × 14.99 + 4 × 20 + 5 × 25)
= 1/25 (402.42)
= 16.09 ≅ 16.1
Therefore, the mean is the same as the mean obtained in option (a).
(d) Calculating the median and the mode:
Since N = 25(odd) i.e., 2· 12 + 1; k = (12 + 1)th term = 13th term
So, the median = 14.99. (frequency at 13th term)
Since the highest frequency is 6 occurred by the cost is $14.99,
Mode = 14.99
Learn more about frequency distribution here:
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