The number of bedrooms of homes in a certain community is shown on the table below.
(a) Find the cumulative distribution for the table.
Number of Bedrooms Percent Cumulative
0 2% 1 .%
1 8% 2 .%
2 24% 3 .%
3 35% 4 .%
4 21% 5 .%
5 7% 6 .%
6 or more 3% 7 .%
(b) Find the mean for the table. (Give the answer to two decimal places.)
8
(c) Find median for the table.
9
(d) Find mode for the table.
10
0
(a) To find the cumulative distribution for the table, we need to calculate the cumulative percent for each number of bedrooms.
Starting with the cumulative percent for 0 bedrooms, we add the percent of 0 bedrooms (2%) to get the cumulative percent for 0 bedrooms: 2%.
Next, for 1 bedroom, we add the percent of 1 bedroom (8%) to the cumulative percent for 0 bedrooms to get the cumulative percent for 1 bedroom: 2% + 8% = 10%.
We continue this process for each number of bedrooms, adding the percent to the cumulative percent from the previous category:
- For 2 bedrooms, cumulative percent = 10% + 24% = 34%
- For 3 bedrooms, cumulative percent = 34% + 35% = 69%
- For 4 bedrooms, cumulative percent = 69% + 21% = 90%
- For 5 bedrooms, cumulative percent = 90% + 7% = 97%
- For 6 or more bedrooms, cumulative percent = 97% + 3% = 100%
So, the cumulative distribution for the table is:
Number of Bedrooms Cumulative Percent
0 2%
1 10%
2 34%
3 69%
4 90%
5 97%
6 or more 100%
(b) To find the mean for the table, we multiply each number of bedrooms by its percent, sum them up, and divide by 100 to get the average.
Mean = (0 x 2% + 1 x 8% + 2 x 24% + 3 x 35% + 4 x 21% + 5 x 7% + 6 or more x 3%) / 100
Mean = 0 + 0.08 + 0.48 + 1.05 + 0.84 + 0.35 + (6 or more x 0.03) / 100
Since the category "6 or more" is not clear, we'll assume it as 6:
Mean = 0 + 0.08 + 0.48 + 1.05 + 0.84 + 0.35 + (6 x 0.03) / 100
Mean = 3.83 / 100 = 0.0383
Hence, the mean for the table is 0.0383 or approximately 0.04.
(c) To find the median for the table, we need to determine the middle category. Since we have 7 categories, the middle category would be the 4th category.
From the table, we can see that the 4th category is 3 bedrooms with a cumulative percent of 69%. Therefore, the median number of bedrooms is 3.
(d) To find the mode for the table, we look for the category with the highest percent. In this case, both the 3 bedrooms and 4 bedrooms categories have the highest percent of 35%.
Therefore, the mode for the table is either 3 bedrooms or 4 bedrooms.