QNT 351 According to the Empirical Rule, what percentage of your

Question:

Based on the results, and information that is included in theexcel attachment. I need help with the following three questions...

1. According to the Empirical Rule, what percentage of your sample means should be within 1 standard deviation of the population mean? Using your computed ??, do your sample means seem to conform to the rule?

2. According to the Empirical Rule, what percentage of your sample means should be within 2 standard deviations of the population mean? Again, do your sample means seem to conform to the rule?

3. You used the Empirical Rule because it really gives us more information (and because I asked you to), but truthfully you should have used Chebyshev's Theorem. Even though Chebyshev's doesn't tell us much, why should you have used that one instead?

Price
Bedrooms Sq Footage Baths
263.1
4
2300
182.4
4
2100
242.1
3
2300
213.6
2
2200
139.9
2
2100
245.4
2
2100
327.2
6
2500
271.8
2
2100
221.1
3
2300
266.6
4
2400
292.4
4
2100
209
2
1700
270.8
6
2500
246.1
4
2100
194.4
2
2300
281.3
3
2100
172.7
4
2200
207.5
5
2300
198.9
3
2200
209.3
6
1900
252.3
4
2600
192.9
4
1900
209.3
5
2100
345.3
8
2600
326.3
6
2100
173.1
2
2200
187
2
1900
257.2
2
2100
233
3
2200
180.4
2
2000
234
2
1700
207.1
2
2000
247.7
5
2400
166.2
3
2000
177.1
2
1900
182.7
4
2000
216
4
2300
312.1
6
2600
199.8
3
2100
273.2
5
2200
206
3
2100
232.2
3
1900
198.3
4
2100
205.1
3
2000
175.6
4
2300
307.8
3
2400
269.2
5
2200
224.8
3
2200
171.6
3
2000
216.8
3
2200
192.6
6
2200
236.4
5
2200
172.4
3
2200
251.4
3
1900
246
6
2300
147.4
6
1700
176
4
2200
228.4
3
2300
166.5
3
1600
189.4
4
2200
312.1
7
2400
289.8
6
2000
269.9
5
2200
154.3
2
2000
222.1
2
2100
209.7
5
2200
190.9
3
2200
254.3
4
2500
207.5
3
2100
209.7
4
2200
294
2
2100
176.3
2
2000
294.3
7
2400
224
3
1900
125
2
1900
236.8
4
2600
164.1
4
2300
217.8
3
2500
192.2
2
2400
125.9
2
2400
220.9
2
2300
294.5
6
2700
244.6
2
2300

2
2
2
2.5
1.5
2
2
2.5
1.5
2
2
1.5
2
2
2
2
2
2.5
2
2
2
2.5
1.5
2
3
1.5
2
2
1.5
2
2
2
2
2
2
2.5
2
2.5
2
3
1.5
1.5
1.5
2
2
3
3
2.5
2
2
2
2
2
2
3
2
2
1.5
2.5
2
3
3
2.5
2
2
2
2
2
2
2
2.5
2
2
2
1.5
2
2
2
2.5
1.5
2
2
2.5

Price Listing Frequency
125
125.9
139.9
147.4
154.3
155.4
164.1
166.2
166.5
171.6
172.4
172.7
173.1
173.6
175
175.6
176
176.3
177.1
179
180.4
182.4
182.7
186.7
187
188.1
188.3
189.4
190.9
192.2
192.6
192.9
194.4
198.3
198.9
199
199.8
205.1
206
207.1
207.5
209
209.3
209.7
213.6
216
216.8
217.8
220.9
221.1
221.5
222.1
224
224.8
227.1
228.4
232.2
233
234
236.4
236.8
240
242.1
243.7
244.6
245.4
246
246.1
247.7
251.4
252.3
253.2
254.3
257.2
263.1
263.2
266.6
269.2
269.9
270.8
271.8
273.2
281.3

Relative
Frequency
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
2 0.01904762
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
2 0.01904762
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
4 0.03809524
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
2 0.01904762
1 0.00952381
2 0.01904762
2 0.01904762
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
2 0.01904762
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381
1 0.00952381

Price Listing
125-145
145-165
165-185
185-205
205-225
225-245
245-265
265-285
285-305
305-325
325-345
345-365
Total

Relative
Frequency
3 0.02857143
4 0.03809524
17 0.16190476
18 0.17142857
20 0.19047619
12 0.11428571
11 0.1047619
7 0.06666667
6 0.05714286
4 0.03809524
2 0.01904762
1 0.00952381
105

Frequency

bin range
125
145
165
185
205
225
245
265
285
305
325
345
365

Histogram
25
20
15

Frequency

10
5
0

Price

Findings
The distribution depicted in the histogram shows some element of
normal distribution as it is almost bell shaped though just slightly skewed
to the left. From the histogram we can tell that the most common price is
in the 205-225 range while the least common price is in the above 345
range.

Bedrooms Bedrooms Frequency
2
2
24
2
3
26
2
4
26
2
5
11
2
6
14
2
7
2
2
8
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5

30
25
20

Frequency 15
10
5
0

2

199
240
263.2
188.1
243.7
221.5
175
253.2
155.4
186.7
179
188.3
227.1
173.6
188.3
310.8
293.7
179
188.3
227.1
173.6
188.3
Mean
221.1029
Median
213.6
Mode
188.3
1st Quartile
187

3
4
4
2
6
4
2
3
4
5
3
6
4
4
5
8
6
3
6
4
4
5

2500
2600
2300
1900
2700
2300
2500
2300
2400
2500
2400
2100
2900
2100
2300
2900
2400
2400
2100
2900
2100
2300
2223.80952
2200
2100
2100

3rd Quartile
251.4
Min
125
Max
345.3
Range
220.3
Variance
2218.919

2400
1600
2900
1300
61831.5018

Standard
Deviation
Chebyshev

47.1054
99.9549%

248.659409
99.9984%

97.515%

99.067%

Empirical
rule

1.5
2
2
1.5
2
2
2
2
2
2.5
2
2
2
2.5
1.5
2
3
2
2.5
1.5
2
3

289.8
292.4
293.7
294
294.3
294.5
307.8
310.8
312.1
326.3
327.2
345.3
Total

1
1
1
1
1
1
1
1
2
1
1
1
105

0.00952381
0.00952381
0.00952381
0.00952381
0.00952381
0.00952381
0.00952381
0.00952381
0.01904762
0.00952381
0.00952381
0.00952381

Findings
Using Chebyshev's theorem, atleast 99.95% of the listing prices lie between -2 and +2
standard deviations from the mean and about 99.998% of the square footages lie between
-2 and +2 standard deviations from the mean.
Using the empirical rule, atleast 97.515% of the listing prices lie between -2 and +2 standard
deviations from the mean and atleast 99.067% of the square footages lie between -2 and +2
standard deviations from the mean.
Comparing with the actual data, we can see that both the listing prices and the square
footages are almost normally distributed since the percentages are close to 95% which is
the percentage for normal distribution. From the histogram, we can also see that the
distribution of listing prices is almost nearly bell shaped though slightly skewed to the left.
Conclusion
From this observation we can conclude that the empirical rule is more accurate as it gives
percentages that are more close to 95% for normal distribution.

5
5
5
5
6
6
6
6
6
6
6
6
6
6
6
6
6
6
7
7
8
8

Bar chart

3

4

5

Bedrooms

6

7

8