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
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