Question

Use this sample of house prices and lot sizes in the Pelham Bay neighborhood of the Bronx from 2018-2019 to answer the questions below.

price	lot size
490000	2503
512000	2483
345000	2500
508670	2900
550000	2513
300000	2513
995000	4950
920000	3135
470000	2375
450000	2375

1. What kind of data is this?
2. For one of the series, and for 3 equally spaced non-overlapping intervals what in the interval size, the beginning, end and midpoint of each interval, the frequency, relative frequency, and cumulative relative frequency of each interval? Sketch the histogram and ogive.
3. What is the maximum, minimum, first quartile, median, third quartile, IQR, range, arithmetic mean, and standard deviation of the ungrouped data?

Answer 1

for Price

class interval	frequency	mid point ,x	class width	frequency	relative frequency=fi/N	cumulative frequency
300000-531699	6	415849.5	231700	7	0.7	7
531700-763399	11	647549.5	231700	1	0.1	8
763400-995099	4	879249.5	231700	2	0.2	10

maximum =    995000
minimum=   300000

quartile , Q1 = 0.25(n+1)th value=   2.75th value of sorted data=   423750
      
Quartile , Q3 = 0.75(n+1)th value=   8.25th value of sorted data=   642500

Median=0.5(n+1)th value =    5.5th value of sorted data=   499335
IQR = Q3-Q1 =    642500-423750=   218750.0
range=max-min =    995000-300000=   695000.000
mean =    ΣX/n =    5540670/10=   554067.00
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √(462436764010/9)=   226675.677