Question

7 S). The following table gives the mean federal tax burden per family in each of states and y in each of the 50 the District of Columbia, in dollars (S), for the 2016 tax season. For the curious,t the lowest is eest Virginia and the highest is Connecticut; Maryland was $14.197, Virgima wa DC was S20,563. 8607 8630 87 993-9964-2988 471 9195 9362. -9619T96301-9793 T9852 99988 10000 10250 10300 10618 10715 10874 mon ,이 10958 111921-112131 11252111264111290 1 1 17441 1 1842 11901 12160 12266 12331 12471 12605 12700 12889 13110 4197 14239 14244 14664 14750 14823 15097 16029 16329 16996 18367 18997 19782 20563 22785 a). Give the 5-Number-Summary b). Test for outliers showing all work

Answer 1

Solution : Given that samples: 8607,8630,8747,9195,9362,9619,9630,9793,9852,9930,9964,9988,10000,10250,10300,10618,10715,10874,10953,10958,11192,11213,11252,11264,11290,11744,11842,11901,12160,12266,12331,12471,12605,12700,12889,13110,14197,14239,14244,14664,14750,14823,15097,16029,16239,16996,18367,18997,19782,20563,22785

a) 5 number summary

Minimum : 8607
Quartile Q1: 10000
Median : 11744
Quartile Q3: 14244
Maximum : 22785

Quartile Q1:

Explanation

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

8607 8630 8747 9195 9362 9619 9630 9793 9852 9930 9964 9988 10000 10250 10300 10618 10715 10874 10953 10958 11192 11213 11252 11264 11290 11744 11842 11901 12160 12266 12331 12471 12605 12700 12889 13110 14197 14239 14244 14664 14750 14823 15097 16029 16239 16996 18367 18997 19782 20563 22785

So, the bottom half is

8607 8630 8747 9195 9362 9619 9630 9793 9852 9930 9964 9988 10000 10250 10300 10618 10715 10874 10953 10958 11192 11213 11252 11264 11290

Quartile Q3 = 14244

Explanation

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

8607 8630 8747 9195 9362 9619 9630 9793 9852 9930 9964 9988 10000 10250 10300 10618 10715 10874 10953 10958 11192 11213 11252 11264 11290 11744 11842 11901 12160 12266 12331 12471 12605 12700 12889 13110 14197 14239 14244 14664 14750 14823 15097 16029 16239 16996 18367 18997 19782 20563 22785

So, the upper half is

11842 11901 12160 12266 12331 12471 12605 12700 12889 13110 14197 14239 14244 14664 14750 14823 15097 16029 16239 16996 18367 18997 19782 20563 22785

The median of these numbers is 14244.

The median of these numbers is 10000.

b) Set of outliers: Q1 - 1.5 × IQR; Q3 + 1.5 × IQR = {20563, 22785}