# D:\jknuba_2025_spring\jknuba_MSC\jknuba_MSC_DOC\
jknuba_MSC_Job3_All.wxmx

kill - Removes all bindings (value, function, array, or rule) from the arguments a_1, …, a_n. An argument a_k may be a symbol or a single array element.

kill(all);

Package stats contains a set of classical statistical inference and hypothesis testing procedures.
Package stats loads packages descriptive, distrib
Package descriptive contains a set of functions for making descriptive statistical computations and graphing. 

load("stats")$

This normally means that a list, a set or something else that consists of more than one element was expected. 

p:[59.39762397483823,    12.68700015685627,    31.35538411535527,    23.1036037153536,    16.39552698454976,    27.01157697689639,    39.8173028014986,    54.71782259683489,    32.86331390184777,    44.10002967620344,    2.365565533494923,    40.64433869221747,    64.59254476151632,    2.703301000039238,    41.12065030882908,    38.55489179860347,    42.55275479744299,    30.59619381218819,    3.375030988193638,    0.1513122243954068,    20.51450025858425,   55.91491920591274,    2.734255975155692,    55.16354628521058,    15.14354144838837,    44.92242265044037,    39.75112753258765,    56.62421750522258,    9.863393407881814,    41.35089981759533,    42.80463303851646,    38.39042860902299,    30.44905471801171,    50.10507869829214,    45.79592830044311,    33.52522232509477,    48.65922943483395,    20.80334721705067,    29.42590881770415,    8.333780516619887,    43.7196955856165,    1.063999940204406,    50.86120105609081,    17.11882275390031,    10.58429445907518,    60.03274138897483,    5.351089442351305,    7.896425257058851,    58.70439635154142,    42.06021218741804,    55.3367642799664,    35.37948530261435,    2.799704152460334,    43.16506440140017,    59.17919419751087,    62.69640197149587,    6.44243467651085,    12.89419376857005,    18.64249519577364,    52.12195830133088,    53.53279479251758,    10.65037878149241,    35.30942715378566,    18.33293003081024,    18.48059931632189,    38.90586123842466,    26.25131184483497,    3.318332682217242,    46.75062151347198,    43.72625516704196,    63.9909979311192,    46.03068974336779,    7.193358353151108,    29.65708334839154,    52.40237751210758,    36.78245806593392,    21.06493261212433,    48.87876636548086,    23.72632507601132,    41.25105453851204,    56.59427438532665,    37.42010498415079,    5.628126184621783,    35.33261368945548,    43.80297624358005,    35.22107942536941,    61.40171930123801,    9.053453438177984,    16.03950951478958,    7.377139957815818,    41.47586339047343,    59.46353293109683,    13.42941713508699,    38.33555283152583,    32.64690943784151,    37.68425793066372,    35.36199757913382,    23.6617856124797,39.42508294452147,    37.82554332062914];

length   -  Returns (by default) the number of parts in the external (displayed) form of expr. For lists this is the number of elements, ...

length (p);

D:\jknuba_2025_spring\jknuba_MSC\_j_Stat_Ebook\jknuba_MSC_Job3\Normal_distribution_pdf.jpg

histogram  -  Constructs and displays a histogram from a data sample. Data must be stored as a list of numbers, ...

histogram ( p, nclasses = 10, title = "Histogram", xlabel = "Values", ylabel = "Count of values", fill_color = red
    , fill_density = 0.4);

Function: smin
    smin (list)
    smin (matrix)

    This is the minimum value of the sample list. 

D:\jknuba_2025_spring\jknuba_MSC\_j_Stat_Ebook\jknuba_MSC_Job3\jknuba_Job3_histogram_pic.svg

smin(p);

Function: smax
    smax (list)
    smax (matrix)

    This is the maximum value of the sample list. 

 smax (p);

This is the sample mean, defined as

                       n
                     ====
             _   1   \
             x = -    >    x
                 n   /      i
                     ====
                     i = 1

 mean(p);

 range - The range is the difference between the extreme values. 

 range(p);

Function: quantile
    quantile (list, p)
    quantile (matrix, p)

    This is the p-quantile, with p a number in [0,1], of the sample list. Although there are several definitions for the sample quantile (Hyndman, R. J., Fan, Y.
(1996) Sample quantiles in statistical packages. American Statistician, 50, 361-365), the one based on linear interpolation is implemented in package
descriptive 

quantile (p, 0);quantile (p, 1/4);quantile (p, 2/4);quantile (p, 3/4);quantile (p, 4/4);smin(p);smax(p);

Function: qrange
    qrange (list)
    qrange (matrix)

    The interquartilic range is the difference between the third and first quartiles, quantile(list,3/4) - quantile(list,1/4), 

qrange (p);

quantile (p, 3/4)-quantile (p, 1/4);

median - Once the sample is ordered, if the sample size is odd the median is the central value, otherwise it is the mean of the two central values.

 median(p);

Function: mean_deviation
    mean_deviation (list)
    mean_deviation (matrix)

    The mean deviation, defined as

                         n
                       ====
                   1   \          _
                   -    >    |x - x|
                   n   /       i
                       ====
                       i = 1

mean_deviation (p);

Function: var
    var (list)
    var (matrix)

    This is the sample variance, defined as

                         n
                       ====
               2   1   \          _ 2
              s  = -    >    (x - x)
                   n   /       i
                       ====
                       i = 1

Function: median_deviation
    median_deviation (list)
    median_deviation (matrix)

    The median deviation, defined as

                     n
                   ====
               1   \
               -    >    |x - med|
               n   /       i
                   ====
                   i = 1

    where med is the median of list. 

 median_deviation (p);

Function: skewness
    skewness (list)
    skewness (matrix)

    The skewness coefficient, defined as

                        n
                      ====
                1     \          _ 3
               ----    >    (x - x)
                  3   /       i
               n s    ====
                      i = 1

D:\jknuba_2025_spring\jknuba_MSC\_j_Stat_Ebook\jknuba_MSC_Job3\jknuba_MSC_Job3_skewness.jpg

 skewness (p);

var(p);

Function: var1
    var1 (list)
    var1 (matrix)

    This is the sample variance, defined as

                         n
                       ====
                   1   \          _ 2
                  ---   >    (x - x)
                  n-1  /       i
                       ====
                       i = 1

var1(p);

Function: std
    std (list)
    std (matrix)

    This is the square root of the function var, the variance with denominator n. 

 std (p);

Function: std1
    std1 (list)
    std1 (matrix)

    This is the square root of the function var1, the variance with denominator n−1. 

std1 (p);

test_mean - This is the mean t-test. Argument x is a list or a column matrix containing an one dimensional sample.

test_mean(p);

test_mean(p ,'conflevel=0.9, 'mean=32.77849275554686);

test_mean(p ,'conflevel=0.95, 'mean=32.77849275554686);

# Відповідь: 
- оцінка форми гістограми;
- порівняти середнє, моду, медіану, коефіцієнт асиметрії
- показати довірчій інтервал.