Question

An auto dealer's sales numbers are shown in the table below. Find for each month the mean, median, and mode prices of the cars she sold. Round your answers to the nearest dollar.

		Number sold
Price	May	June	July
$25,000	22	25	24
$15,000	49	24	24
$13,500	25	49	49

May

mean	$
median	$
mode	$

June

mean	$
median	$
mode	$

July

mean	$
median	$
mode

Answer 1

We have to find the mean, median and mode for each of the months May, June and July. So, let us make different tables for all the three months.

For May :

Price (x)	Frequency (f)	Cumulative Frequency (cf)	f*x
$25000	22	22	550000
$15000	49	71	735000
$13500	25	96	337500
Total	96		1622500

We know, Mean = = 1622500/96 = 16901.0417(rounded up to four decimal places).

Now, for finding the median, we will first divide the total frequency by 2. Here, total frequency = 96.

Thus, there are 96 scores. Dividing by 2, we get, 96/2 = 48. Thus, the median is the average of 48th and 49th number(as the number of scores are even).

For finding the 48th and 49th score, we will check the cumulative frequency table. In the cumulative frequency, the second row gives 71 and the first row gives 22. Thus, 48th and 49th lies between 1st and 2nd row. So, we can easily say that the 48th and 49th score is $15000. Thus, the median is average of $15000 and $15000. Thus, Median = $(15000+15000)/2 = $15000.

We know, the value which occurs maximum number of times is called the mode. Here, $15000 has occurred the maximum number of times (i.e., 49 times). Thus, the mode is $15000.

Thus, for May, Mean = $16901.0417, Median = $15000 and Mode = $15000.

For June :

Price(x)	Frequency (f)	Cumulative Frequency (cf)	f*x
$25000	25	25	625000
$15000	24	49	360000
$13500	49	98	661500
Total	98		1646500

We know, Mean = = 1646500/98 = $16801.0204(rounded up to four decimal places).

Now, for finding the median we will divide the total frequency by 2. Here, total frequency = 98(even).

Thus, dividing 98 by 2, we get 98/2 = 49. Thus, the median is the average of 49th and 50th score. From the cumulative frequency, we can see that the second row gives 49 and the third row gives 98. Thus, we can understand that the 49th score is $15000 and the 50th score is $13500. Thus, the median is the average of $15000 and $13500. Thus, Median = $(15000+13500)/2 = $(28500/2) = $14250.

Thus, Median = $14250 .

We know that the value which occurs maximum number of times is called the mode. Here, $13500 has occurred maximum number of times (i.e., 49 times). Thus, the mode is $13500 .

Thus, for June, Mean = $16801.0204, Median = $14250 and Mode = $13500 .

For July :

Price (x)	Frequency (f)	Cumulative Frequency(cf)	f*x
$25000	24	24	600000
$15000	24	48	360000
$13500	49	97	661500
Total	97		1621500

We know, Mean = = 1621500/97 = $16716.4948(rounded up to four decimal places).

Now, for finding the median, we will first divide the total frequency by 2. Here, the total frequency is 97(odd).

Thus, dividing 97 by 2, we get 97/2 = 48.5 . Thus, we will round 48.5 to the nearest integer. Thus, rounding 48.5 to the nearest integer, we get 49. Thus, the median is the 49th score. We will check the cumulative frequency to find the 49th score. In the cumulative frequency, the second row gives 48 and the third row gives 97. Thus, the 49th score lies in between the second and third row. So, following the corresponding frequency, we can say that the 49th score is $13500 . Thus, the median is $13500.

We know, the value which occurs maximum number of times is called the mode. Here, $13500 has occurred maximum number of times (i.e., 49 times). Thus, the mode is $13500.

Thus, for July, Mean = $16716.4948, Median = $13500 and Mode = $13500 .